This is a manual tiling puzzle. Difficulty level always hard to estimate, but I would say a few minutes per solution for an accomplished solver, all the way to just about impossible for someone like me. I always reach for the computer.
The goal is to tile all twelve '4x inflated pentominoes'. Ie take a pentomino and scale it up by a factor of four in each dimension. The five squares of the pentomino become five 4x4 squares. Each inflated pentomino is to be tiled with a full set of normal sized pentominoes (12) and tetrominoes (5). Tiled means covered with no gaps or overlaps. The pieces may be flipped. There are one or two additional constraints.
- No tetromino is allowed to touch another, even at a corner.
- With exceptions, tetrominoes are not allowed to touch the edge. For internal corners they are allowed to be diagonally adjacent.The list of exceptions for each inflated pentomino is below.
P: no tetromino touches the edge (4 solutions)
I: both L4 and T4 allowed to touch the edge) (5 solutions)
T: L4 touching the edge (10 solutions)
L: L4 touching (2 solutions)
W: N4 touching (1 solution)
V: I4 touching (9 solutions)
Z: I4 touching (7 solutions)
X: I4 touching (9 solutions)
U: I4 touching (4 solutions)
N: O4 touching (2 solutions)
Y: O4 touching (2 solutions)
F: O4 touching (3 solutions)
For illustration, a sample solution for 'T'. Pentominoes and tetrominoes both labelled so you can tell what the labelling in the list above means. eg 'N4' means the blue piece labelled 'N'. Note that tetrominoes are allowed to touch an internal corner diagonally as N4 does in this solution.